向量高斯信道上LTI源的线性编码：一种优化方法
Linear Coding of LTI Sources Over Vector Gaussian Channels: A Majorization Approach
- Peking University（北京大学）
- Guangxi University（广西大学）
- Institute of Science Tokyo（东京科学大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究针对带反馈的功率约束并行高斯信道，提出LTI编解码器对的设计方法，推导了两种功率约束下的充要条件与最优功率分配方案，明确了传输难度的影响因素。
AI中文摘要：
我们研究了线性时不变（LTI）编解码器对的设计，该编解码器用于在带反馈、受功率约束的并行高斯信道上传输离散时间LTI向量源的状态。考虑了两种类型的功率约束：在子信道功率单独约束下，通过涉及子信道信噪比和源的反稳定极点的两个耦合优化不等式，建立了实现有界估计误差协方差（EEC）的编解码器对设计的充要条件；在总信道功率约束下，利用优化序下的偏序规划推导了可行编解码器设计所需的最小总功率。对于噪声方差相等的情况，得到了解析形式的最优功率分配，其具有注水法的解释；对于一般噪声情况，开发了顺序注水法。我们的结果表明，通过LTI编码传输离散时间LTI源的难度不仅取决于其拓扑熵，还取决于其反稳定极点对数幅度的均匀性，同时也提供了可行编解码器对的设计方法。
英文摘要：
We study the design of linear time-invariant (LTI) encoder-decoder pairs for transmitting the state of a discrete-time LTI vector source over power-constrained parallel Gaussian channels with feedback. Two types of power constraints are considered. Under individual subchannel power constraints, a necessary and sufficient condition for designing an encoder-decoder pair that achieves bounded estimation error covariance (EEC) is established via two coupled majorization inequalities involving the subchannel signal-to-noise ratios and the antistable poles of the source. Under total channel power constraint, we derive the minimum total power required for a feasible encoder-decoder design by exploiting partial-order progamming under majorization order. An analytical optimal power allocation is obtained for the case of equal noise variances, which admits a water-filling interpretation; for general noise case, a sequential water-filling algorithm is developed. Our results reveal that the difficulty of transmitting a discrete-time LTI source via LTI coding is governed not only by its topological entropy, but also by the evenness of the log-magnitudes of its antistable poles. The design methods for feasible encoder-decoder pairs are also provided.
